Math. Model. Nat. Phenom.
Volume 14, Number 1, 2019
Economics and the environment: distributed optimal control models
|Number of page(s)||23|
|Published online||02 April 2019|
A model in continuous time and space to study economic migration
CNRS at Paris School of Economics,
48 Boulevard Jourdan,
2 THEMA, University of Cergy-Pontoise, 95011 Cergy-Pontoise, France.
3 Ecole Polytechnique, 91128 Palaiseau, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 13 December 2018
Population movements modify the environment, land-use, and shape the landscape through urbanization. Furthermore, migration has become one of the most relevant determinants of global human health and social development. The objective of this paper is to provide a framework to understand the economic and natural factors responsible for migration and population agglomerations and their environmental consequences. In this regard, we develop an economic model in continuous time and space adapting Hotelling’s migration law to make individuals react to possible improvements of their welfare. First we show that there is solution to this spatial-dynamic problem. Then, we illustrate the properties of the economy and the associated population dynamics through numerical simulations.
Mathematics Subject Classification: 49J20 / 49K20 / 91B55 / 91B62 / 91B72
Key words: Migration / spatial dynamics / economic growth / parabolic PDE
© EDP Sciences, 2019
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